Just tacking on to Mark's comments, a big difference in the systems is the maps. In the HPS titles there are a lot more of them, and the vast majority of them are significantly larger. So not only does this give you more options on scenarios and different ground to fight on, it also makes you think a bit more when fighting.
For example, take the Talon Gettysburg battle and the HPS Gettysburg battle. The map for the HPS game is easily 10 times the size of the Battleground one. So there's no map edge to anchor a flank on. You must use scouting efficiently (which encourages the historic use of cavalry), you must maintain a reserve, as there's no telling where you might need it, and it's quite possible to disengage from one battle only to have to fight another before you get the chance to consolidate. And, on meeting engagements it gives you the opportunity to choose your ground.
Additionally, with Talon you got one battle, and maybe some small action that was "close by". In HPS you get an entire campaign worth of content, in same cases over a dozen battles.
Some other difference are the ability to play on-line in a multiplayer fashion. I've played games with 2 guys per side, both guys on a team are able to do all their movements, etc. at the same time greatly speeding up game play.
I know there's other differences too, but it's been almost 2 years since I played the BG games, so I can't remember any more right now. However my vote is hands-down HPS over the Talonsoft titles.